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Abstract

Toroidal multipoles are the subject of growing interest because of their unusual electromagnetic properties different from the electric and magnetic multipoles. In this paper, we present two new related classes of plasmonic metamaterial composed of purposely arranged of four U-shaped split ring resonators (SRRs) that show profound resonant toroidal responses at optical frequencies. The toroidal and magnetic responses were investigated by the finite-element simulations. A phenomenon of reversed toroidal responses at higher and lower resonant frequencies has also been reported between this two related metamaterials which results from the electric and magnetic dipoles interaction. Finally, we propose a physical model based on coupled LC circuits to quantitatively analyze the coupled system of the plasmonic toroidal metamaterials.

Fig. 2 Simulated transmittance and reflectance spectra of TM1 (a) and TM2 (d). The superscript “+” and “-” correspond to the higher and lower energy levels of each TM. The subscript “M ” and “T ” corresponding to magnetic resonance and toroidal resonance, respectively. Dispersion of radiated powers of various multipole moments for TM1 (b) and TM2 (e). Hybridization model of metamolecules for TM1 (c) and TM2 (f). The resonance energy of two-up U-shaped SRRs and two-down U-shaped SRRs are degenerated. Due to the coupling effect of SRRs, the energy level of degenerated resonance mode are split into toroidal and magnetic resonance. It’s notably that the splitting of energy level in the case of TM1 is larger than that of TM2, and the toroidal resonance of TM1 is excited at higher frequency than that of TM2.

Fig. 3 Magnetic energy (color map, in logarithm scale), streamline of magnetic field (black line) and current density of z-component distributions (shown in color in second row) at respective resonances for the TM1 (a) and TM2 (b). The third row: schematic diagram of generated magnetic resonance (M) and toroidal resonance (T) in the case of TM1 and TM2. The magnetic dipole and surface current of a SRR are shown in red and blue arrow, respectively. The lowest row: schematic diagram of the electric (in blue arrow) and magnetic (in red arrow) dipoles interactions, which can explain the resonant modes in higher or lower energy.

Fig. 4 Simulated transmission spectra as a function of radius r of TM1 (a) and TM2 (b). (c) The normalized coupling coefficients as a function of radius r obtained from the resonance frequencies in (a) and (b).